If JK = x + 8, KL = 10, and JL = 7x, what is JK?

Answer:

===============================

Use angle addition postulate:

Substitute the values and solve for x:

Find the angle measures:

Answer:

[tex] \sf \large \: x≤6 \: or \: x≥10[/tex]

Step-by-step explanation:

Let's solve your inequality step-by-step.

x2−16x+60≥0

Let's find the critical points of the inequality.

x2−16x+60=0

(x−6)(x−10)=0(Factor left side of equation)

x−6=0 or x−10=0(Set factors equal to 0)

x=6 or x=10

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤6(Works in original inequality)

6≤x≤10(Doesn't work in original inequality)

x≥10(Works in original inequality)

The type of model that would be the most appropriate would be the exponential model: An exponential model is appropriate because the relationship between days and the natural log of views is linear, and the residual plot does not show a clear pattern.

This is the term that is used to refer to the process that is known to show a growth that is double its rate of growth. That is, it is used to show that there is the existence of a speed up in the rate at which the data is growing and it would follow a particular patter. This can be shown as:  y = ab^x.

This is the term that is used to show the graphical representation that is done by showing the existing relationship that exists between two variables in a graph. That would be the x variable and the y variable.

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Answer:

  70

Step-by-step explanation:

You want the number of paths from corner to corner on a 5×5 grid with no backtracking.

The geometry of the problem matches that of Pascal's triangle, attached.

In the attached figure, the value at each node is the sum of the values above and to the left. This matches the counting process for paths that can be used to get to any particular point on the grid: the total number of ways to get there is the sum of the ways it can be approached from above and the ways it can be approached from the left.

The given grid has some numbers filled in. If we continue to assign values to nodes that are the sum of the values above and to the left, we find the node values match the upper left 5×5 array of values in the attachment.

The value at the lower right corner of that array is 70. That is, ...

there are 70 ways to get from A to B.

__

Alternate solution

The path taken will always have 8 steps. Of those, 4 must be to the right, and 4 must be down. The number of ways we can choose 4 of those 8 steps to be steps to the right is "8 choose 4" ...

  C(8,4) = 8!/(4!(8-4)!) = (8·7·6·5)/(4·3·2·1) = 70

Of course, using Pascal's triangle is simply another way to find the value of C(n,k).

Answer: g(x)=2x-3

Step-by-step explanation:

f(x)=2x-9

g(x)=2x-9+6 ==> Translate 6 units up

g(x)=2x-3

Answer:

In standars form it would look like so:

28,936

In expanded form it would look like so:

20,000 + 8,000 + 900 + 30 + 6

Step-by-step explanation:

Your welcome! Hope it helps! =D

The slope of the lined graph is 5 / 3

The formula for determining the slope of a line is expressed as;

Slope = y2 - y1/ x2 - x1

From the graph shown;

Now, let's substitute the values

Slope, m = 4 - (-1) / 3 - 0

Find the differences

Slope, m = 4 + 1/ 3

Slope, m = 5 / 3

Thus, the slope of the lined graph is 5 / 3

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The number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

It should be noted that ablack drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. The expression will be:

1170 - 64m

The white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. This will be 966 - 52m where m = number of minute

Therefore, we will equate both equations. This will be:

1170 - 64m = 966 - 52m

Collect like terms

-64m + 52m = 966 - 1170

12m = 204

Divide

m = 204 / 12

m = 17

Therefore, the number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

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The length of the rectangle is 21 cm and the width is 16 cm.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The perimeter of the rectangle is defined as the sum of all the sides of the rectangle.

The formula to calculate the perimeter is,

P = 2 ( L + W)

Here

P  = Perimeter

L  = length of the rectangle

W = Width of rectangle

Given that the length of a rectangle is 7 cm more than the width. The perimeter is 78 cm.

The equations can be formed as,

L = 7 + W

P = 2(L+W)

78 = 2 ( 7  + W + W )

39 = 7 + 2W

W = 32/2

W = 16 cm

L = 7 + W

L = 7 + 16 = 21 cm

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The evaluation of function will give the result f(3) = 1

To find the value of function given in question, we will simply keep the desired value in place of variable x.

Rewriting the equation

f(3) = 2x - 5

Keep the value of x in equation, as given in question

f(3) = 2×3 - 5

Performing multiplication to find the value of x in equation given in question

f(3) = 6 - 5

Performing subtraction to find the value of x in equation given in question

f(3) = 1

Therefore, the result of evaluation of given function is f(3) = 1.

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Answer:

25 Hours

Step-by-step explanation:

It says it in the text

Answer:

Step-by-step explanation:

The number of monthly calls for which Plan 1 is more economical than Plan 2 is 200 calls

If more than 200 calls are made, the plan 1 charge will be more than plan 2.

Let the number of charges per month be x

If plan 2 charges ​$16 per month plus ​$0.04 per call, this is expressed as 0.04x + 16

Price that pan 1 charges = $24

If Plan 1 is more economical than Plan 2, this is expressed as:

0.04x + 16 > 24

Subtract 16 from both sides:

0.04x + 16 - 16 > 24 - 16

0.04x > 8

x = 6/0.04

x = 200

This shows that if more than 200 calls are made, the plan 1 charge will be more than plan 2.

We need to know about a composite bar chart to solve the question. The answer for (a) is Tim received 8 texts on Monday, (b) Tim received 4 emails on Thursday and (c) 0.52 of the messages were emails.

A composite bar chart is used when there are two sets of data that are connected and their frequencies are combined.In this question there are two sets of data emails and texts but both of them belong to the same category which is messages. For question (a) we can easily say from the diagram that the number of texts Tim received on Monday is 8.

For question (b) we need to find out the number of emails Tim received on Thursday, for this we have to look at the bar for Thursday and subtract the number of texts received from total number of messages to get the number of emails received that means, 15-11=4, so Tim received 4 emails on Thursday.

For question (c) we need to find the total number of messages received by Tim for five days, total number of emails received and then calculate the fraction of emails out of messages.

Total number of messages=14+16+14+15+14=73

Total number of emails=6+10+10+4+8=38

Fraction of emails over messages=[tex]\frac{38}{73}[/tex]=0.52

Thus 0.52 of the messages were emails.

We analysed the composite bar chart to find out the answers of the three questions, Tim received 8 texts on Monday,4 emails on Thursday and 0.52 of the messages were emails.

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Answer:

a= 5

b= 7

c=

Step-by-step explanation:

The residual plot represents a linear model because (a) there is no clear pattern

The given parameters are:

The graph

The table

For a residual plot to represent a linear model, the following must be true

The points on the residual plot must be randomly dispersed on the plot

This means that all residual plots that have random points are linear models

From the attached graph, we can see that the points on the graph are randomly dispersed

Hence, the residual plot represents a linear model because (a) there is no clear pattern

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1) (c) The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ –11}.

2) (d) The x-intercepts of the graph of the function f(x) = x² + 4x - 12 are ( - 6, 0) and ( 2, 0 ).

1). A parabola opens upward and it passes through ( - 3, 0) and ( 1, 0), and has vertex at ( - 1, - 11 ).

We have the function for the parabola f(x) = 3x² + 6x - 8.

Vertex and the coefficient of the quadratic term are two features of a parabola that aid in determining its range.

Therefore, the critique point of the range and a portion of the constraint is the vertex's vertical coordinate. The next step is to determine if the parabola is concave up or down. The parabola is concave up in this issue if the coefficient of the quadratic terms is positive. As a result of the parabola's concave upward shape, all real numbers greater than - 11 fall into the function's permissible range.

Hence, the range of the function is {y|y ≥ –11}.

2). The graph of the function with the equation f(x) = x² + 4x - 12 is a parabola that opens upward, passes between the points ( - 6, 0) and ( 2, 0), and its vertex is at ( - 6, 0). ( - 2, - 16). It is the y-intercept ( 0, - 12).

The x-intercepts are the locations where the graph and x-axis meet. The y-coordinate of these points is always zero. A parabola can only have two x-intercepts at most. As we can see, the parabola passes through the points ( - 6, 0) and ( 2, 0), and have y coordinates 0, hence the x-intercepts are ( - 6, 0) and ( 2, 0).

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The complete question is mentioned below:

1. On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 1, negative 11), and goes through (1, 0).

What is the range of the function f(x) = 3x² + 6x – 8?

(a) {y|y ≥ –1}

(b) {y|y ≤ –1}

(c) {y|y ≥ –11}

(d) {y|y ≤ –11}

2. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 16), has a y-intercept at (0, negative 12), and goes through (2, 0).

What are the x-intercepts of the graph of the function f(x) = x² + 4x – 12?

(a) (-6, 0), (2,0)

(b) (-2, -16), (0, -12)

(c) (- 6, 0), ( - 2, - 16),

(d) ( 2, 0) (0, -12),

(e) ( - 6, 0), (2, 0)

The equation that models the data will be y = 3 + x and for x = 12, y will be 15.

We are given the equation:

y = a + b x

Also, we have some points of the equation as:

X         2         3         4         5         6           8

Y         5         6         8         9         10         12​

For the point ( 2 , 5 ), we have the equation as:

5 = a + b ( 2 )

5 = a + 2 b

a = 5 - 2 b   …(1)

For the point (3 , 6), we have the equation as:

6 = a + b (3)

6 = a + 3 b

a = 6 - 3 b   …(2)

From (1) and (2), we get that:

5 - 2 b = 6 - 3 b

3 b - 2 b = 6 - 5

b = 1

a = 5 - 2

a = 3

So, the equation will become:

y = 3  +  x

For x = 12, we get the value of y as:

y = 3 + 12

y = 15

Therefore, we get that, the equation that models the data will be y = 3 + x and for x = 12, y will be 15.

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Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. We can simply write this statement in mathematical form as,

Total distance covered by Zendaya in 3 hours on her roller skates = $( 5 + ( 3/7 )  of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( ( 35 + 3)/7 ) of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( 38/7 )

Total distance covered by Zendaya in 1 hours on her roller skates = $ (( 38/7 )/3 ) = $ (38/21) of a mile

or we can write also write  ( 38 /21 ) miles per hour as ( 1 and 17/21 ) miles per hour.

So, Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

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The function that is positive for the entire interval [-3,-2] is given by:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

We have to look at the graph of the function relative to the x-axis, as follows:

The graphs for this function are given at the end of the answer, and the only function for which it is positive, that is, above the x-axis, in the entire interval [-3,-2] is the second, hence the correct option is:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

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Answer: 1/9

Step-by-step explanation:

The area of the shaded region is [tex](4/2)^2 \pi =4\pi[/tex]

The area of the entire circle is [tex](6)^2 \pi=36\pi[/tex]

So, the probability is [tex]\frac{4\pi}{36\pi}=1/9[/tex]

Answer:

D = 0.4(L)

Step-by-step explanation:

D = 0.4(L)

Answer: 0.4L=d  

Step-by-step explanation:

40%=0.4

0.4L=d    ==> 40% of L, the listed price, is d, the discount.

Answer:

Step-by-step explanation:

11x+90=15x

The computation shows that Michael will take 22.5 hours to paint a similar sized house working

Based on the information given, the appropriate equation to use will be:

= 1/15 + 1/18 + 1/Michael = 1/6

Add the two fractions on the left

11/90 + 1/Michael = 1/6

1/Michael = 1/6 - 11/90

Take the reciprocal

Michael = 45/2

Michael= 22.5

Michael will take 22.5 hours.

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Answer:

3.57

Step-by-step explanation:

25/7 is the same as 25÷7 which is 3.57

Answer:

the line runs that aligns with the y-intercept

Step-by-step explanation:

Answer:

[tex]77, 385[/tex]

Step-by-step explanation:

Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.

One number is one-fifth of the other number:

[tex]x=\frac{1}{5}y[/tex]

The difference between the two numbers is 308:

[tex]y-x=308[/tex]

This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.

Now we have a system of equations:

[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]

I will rewrite the first equation for simplicity:

[tex]5x=y[/tex]

Now, I will substitute y from the first equation for y in the second equation:

[tex]5x-x=308[/tex]

Simplify:

[tex]4x=308\\x=77[/tex]

Now, use x to find y using the second equation:

[tex]y-77=308\\y=385[/tex]

Now, I can check the solutions by plugging them into the first equation!

[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]

The solution is correct!

Answer:

11

m/1= 100, m/2 = 80, m/3 = 100

12

m/1 = 47, m/2= 133, m/3=47

Step-by-step explanation:

Number 11 uses Cointerior angle rule

Number 12 uses Cointerior angle rule and Corresponding angle rules

Answer:

Marvin

Step-by-step explanation:

Kelly works four hours a day on tickets and solves on average 38 tickets per day.

38 tickets / 4 hours = 9.5 tickers per hour

_____________________

Brian works five hours per day and solves 45 tickets per hour.

45 tickets / 5 hours = 9 tickers per hour

_____________________________

Marvin works six hours a day on tickets and solves on average 59 tickets per day.

59 tickets / 6 hours = 9.83333 tickers per hour

______________________

Linda works five and a half hours a day on tickets and solves 53 tickets per day.

53 tickets / 5.5 hours = 9.6363637 tickers per hour

Who solves the most tickets per hour? Marvin at 9.833 tickets an hour

Answer: The answer for question 48. is -9, The answer for question 49. is 1/2, the answer for question 50. is -2.25, and for question 51 it's 4/5

Step-by-step explanation:

How to solve question 48

1/2(-12-6)-3(5-3)

-6+3-15+9

-3-6

-9

How to solve question 49

(20/2)+10/(-10+20+30)

10+10/40

20/40

1/2

How to solve question 50.

3/4(-15+4)+(8+7)/(-3)

-45/4+3+15/-3

-11.25+3+15/-3

6.75/-3

-2.25

How to solve question 51

5(7)-(3+4)/-2^2-2^2+3^2

35-7/4+4+27

28/35

4/5

Hope this helped owo